Flow of a thin ribbon of molten glass on a bath of molten tin
Sangweni, Zinhle Brighty
The equations for the flow of a thin lm of molten glass on a bath of molten tin are extended to the case in which the viscosity of the molten glass depends on the temperature. The continuity equation for an incompressible fluid, the Navier-Stokes equation and the energy balance equation are written in the lubrication (thin fluid lm) approximation. The kinematic boundary condition and the boundary conditions for the normal and tangential stress and the normal heat flux are derived on the upper and lower surfaces of the glass ribbon. It is found for the lubrication approximation that only one equation is obtained for four unknowns which are the two horizontal velocity components, the absolute temperature difference and the thickness of the molten glass rib- bon. The remaining three equations are obtained by taking the calculation to the next order in the square of the ratio of the thickness to length of the glass ribbon. The kinematic edge condition and the edge conditions for the normal and tangential stress and the normal heat flux are derived. The four edge conditions and the boundary conditions at the inlet and outlet give the boundary conditions for the four partial differential equations. It is not the aim of the dissertation to solve the boundary value problem which has been derived, either numerically or analytically.
A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, for the degree of Master of Science. School of Computer Science and Applied Mathematics. November 7, 2016.
Sangweni, Zinhle Brighty (2016) Flow of a thin ribbon of molten glass on a bath of molten tin, University of Witwatersrand, Johannesburg, <http://wiredspace.wits.ac.za/handle/10539/21677>